Fourth dimension

“ Suppose a person of the Fourth Dimension, condescending to visit you, were to say, ‘Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you infer a Solid (which is of Three) ; but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.’ What would you say to such a visitor? ”

“ To examine the actions of the very small portions of matter with the view of ascertaining if there is any evidence in the phenomena for the supposition of a fourth dimension of space, we must commence by clearly defining what the laws of mechanics would be on the supposition of a fourth dimension. It is of no use asking if the phenomena of the smallest particles of matter are like—we do not know what. ”

“ And in that light we have to regard what of worth and meaning the Exposition has for us.
Although the scientist has found it useful on occasion to postulate the fourth dimension, he has not thought necessary as yet to put it in the category of reality; much less has the layman. Consequently the mathematician holds the sole title to its knowledge unless we recognize the claims of the medium to a fourth-dimensional insight.
There is much, however, today which points to our coming to such perception as the natural result of our evolution and quite apart from geometrical abstractions or occultism. ”

“ To the question, where and what is the fourth dimension, the answer must be, it is here—in us, and all about us—in a direction toward which we can never point because at right angles to all the directions that we know. ”

“ There are two directions of inquiry in which the research for the physical reality of a fourth dimension can be prosecuted. One is the investigation of the infinitely great, the other is the investigation of the infinitely small. ”

“ The method necessarily to be employed in the search for the evidences of a fourth dimension, consists primarily in the formation of the conceptions of four-dimensional shapes and motions. When we are in possession of these it is possible to call in the aid of observation, without them we may have been all our lives in the familiar presence of a four-dimensional phenomenon without ever recognising its nature. ”

“ If you were to step straight out of the looking-glass every one would think you left-handed. Such a change could be accomplished by revolving you in the fourth dimension, and in no other way. Therefore a mirror will show you at any moment exactly the effect of a fourth dimension. Then why is this not a proof of the actual existence of a fourth dimension? ”

“ And as the plane being had to suppose something which prevented his moving off in the third, the unknown dimension to him, so we have to suppose something which prevents us moving off in the direction unknown to us. This something, since we must be in contact with it in every one of our movements, must not be a plane surface, but a solid; it must be a solid, which in every one of our movements we are against, not in. It must be supposed as stretching out in every space dimension that we know; but we are not in it, we are against it, we are next to it, in the fourth dimension. ”

“ We might then suppose that the matter we know extending in three dimensions has also a small thickness in the fourth dimension; that solids are rigid in the fourth as in the other three dimensions; that liquids are too coherent to admit of their spreading out in space, and becoming thinner in the fourth dimension, under the influence of an attractive center lying outside of our space ”

“ The fourth dimension is a form of duration in some way correlated with space. I shall have to work that out in the light of the greater knowledge, which Her vanished Majesty has given me, and which I almost attained to in Egypt. Wherefore, existence in a state of four dimensions, or the world of N^4, as I have always called it, is, roughly speaking, one. Time and space are, as it were, two sides of the same shield, and a person living in that world can see both of them at once. Wherefore, past, present, future, length, breadth, thickness, here and there are all the same thing to him. ”

“ To take one of the conceptions we have already formed, the turning of a real thing into its mirror image would be an occurrence which it would be hard to explain, except on the assumption of a fourth dimension.
We know of no such turning. But there exist a multitude of forms which show a certain relation to a plane, a relation of symmetry, which indicates more than an accidental juxtaposition of parts. ”

“ And in the first place, a being in four dimensions would have to us exactly the appearance of a being in space. A being in a plane would only know solid objects as two-dimensional figures—the shapes namely in which they intersected his plane. So if there were four-dimensional objects, we should only know them as solids—the solids, namely, in which they intersect our space. Why, then, should not the four-dimensional beings be ourselves, and our successive states the passing of them through the three-dimensional space to which our consciousness is confined? ”

“ A cube of three-dimensional matter, since it extends to no distance at all in the fourth dimension, would instantly disappear, if subjected to a motion transverse to our space. It would disappear and be gone, without it being possible to point to any direction in which it had moved.
All attempts to visualise a fourth dimension are futile. It must be connected with a time experience in three space.
The most difficult notion for a plane being to acquire would be that of rotation about a line. Consider a plane being facing a square. ”

“ The Higher Space Hypothesis is of assistance here. It is only necessary to remember that from the fourth dimension the interior of a solid is as much exposed as the interior of a plane figure is exposed from the region of the third dimension. A four-dimensional being would experience no difficulty, under suitable conditions, in possessing itself of any part of the bodily mechanism of another. ”

“ We are as unable to imagine it as a creature living in the plane figure 2 would be to imagine a direction such that moving in it the square 2 would become the cube 3. The third dimension to such a creature would be as unintelligible as the fourth is to us. And at this point we have to give up the aid that is to be got from any presentable object, and we have simply to investigate what the properties of the simplest figure in four dimensions are, by pursuing further the analogy which we know to exist between the process of formation of 2 from 1 and of 3 from 2, and finally of 4 from 3. ”

“ But although this supposition might be worked out at some length, it is hard to suppose that it could afford any definite test of the physical existence of a fourth dimension. No test has been discovered which is decisive. ”

“ The fourth dimension is just as much here as anywhere else. Right here around you and me things exist and go forward in the fourth dimension: but we do not see them and are not conscious of them, because we are confined to our own three. Secondly: if we name the four coordinates as Einstein does, x, y, z, and t, then we exist in x, y, and z, and move freely about in them; but are powerless to move in t. ”

“ If four dimensions exist and we cannot perceive them, because the extension of matter is so small in the fourth dimension that all movements are withheld from direct observation except those which are three-dimensional, we should not observe these double rotations, but only the effects of them in three-dimensional movements of the type with which we are familiar. ”

“ When we speak of the fourth dimension, what we mean is the fourth stage in the apprehension of that infinity. We might as legitimately speak of a fifth dimension, but the profitlessness of any discussion of a fifth and higher stages lies in the fact that they can be intelligently approached only through the fourth, which is still largely unintelligible. ”

“ Thus we can imagine a plane world, in which all the variety of motion is the phenomenon of structures consisting of filamentary atoms traversed by a plane of consciousness. Passing to four dimensions and our space, we can conceive that all things and movements in our world are the reading off of a permanent reality by a space of consciousness. Each atom at every moment is not what it was, but a new part of that endless line which is itself. ”

“ I could easily enough hint at it or suggest it—any fool can do that—but I wanted actually to describe it. To describe a color that is not a color! a form that is formless! A mathematician could perhaps slightly more than suggest it. There would be strange curves and angles that an inspired mathematician in a wild frenzy of calculation might glimpse vaguely. It is absurd to say that mathematicians have not discovered the fourth dimension. They have often glimpsed it, often approached it, often apprehended it, but they are unable to demonstrate it. ”

“ In other words, time is made the fourth dimension. Psychic phenomena indicate that occasionally, in some individuals, the will is capable of producing physical movements for whose geometrico-mathematical definition a four-dimensional system of co-ordinates is necessary. ”

“ If we think of a man as existing in four dimensions, it is hard to prevent ourselves from conceiving him prolonged in an already known dimension. The image we form resembles somewhat those solemn Egyptian statues which in front represent well enough some dignified sitting figure, but which are immersed to their ears in a smooth mass of stone which fits their contour exactly. ”

“ Such a being would be able to make but a part of himself visible to us, for a cube would be apprehended by a two-dimensional being as the square in which it stood. Thus a four-dimensional being would suddenly appear as a complete and finite body, and as suddenly disappear, leaving no trace of himself, in space, in the same way that anything lying on a flat surface, would, on being lifted, suddenly vanish out of the cognizance of beings, whose consciousness was confined to the plane. ”

“ I prefer, therefore, in proposing to consider Time as a fourth dimension of our existence, to speak of it as a fourth dimension rather than the fourth dimension. Since this fourth dimension cannot be introduced into space, as commonly understood, we require a new kind of space for its existence, which we may call time-space. There is then no difficulty in conceiving the analogues in this new kind of space, of the things in ordinary space which are known as lines, areas, and solids. A straight line, by moving in any direction not in its own length, generates an area ”

“ Discarding experience and reasoning wholly from analogy, we introduce some properties of the fourth dimension as follows.
Four-dimensional measure depends upon length, breadth, height and a fourth dimension all multiplied together. In the graphical representation of -space, points are referred to three mutually perpendicular planes formed by three lines mutually at right angles. In a similar way, to represent -space we must assume another axis at right angles to each of the other three. ”

“ It may be that in the very large or the very minute a fourth dimension of space will have to be postulated to account for parts—but with regard to objects of ordinary magnitudes we are certainly not in a four dimensional world. ”

“ If any real existence confined to a superficies could be shown to exist, there would be an argument for one relative to which our three-dimensional existence is superficial. But, both on the one side and the other of the space we are familiar with, spaces either with less or more than three dimensions are merely arbitrary conceptions. ”

“ There is a strange delusion that the fourth dimension must be something wholly beyond the conception of the ordinary man, and that only the mathematician can be initiated into its mysteries. It is true that the mathematician has the advantage of understanding the technical machinery for solving the problems which may arise in studying the world of four dimensions ”